I am studying financial engineering and there has been one topic that has been bothering me; Probability.
Here is a question I found at the quant forum.
If a family has two children and there is a boy in the family, what is the probability that there is a girl?
What’s the answer? 2/3.
Or how about coin flipping?
What’s the probability of getting 5 heads in a row before getting 2 tails in a row? fairness is assumed.
What’s the answer? 3/34.
I don’t agree with the answers. Ok, let me reiterate this clearly I don’t agree with the mathematics that came up with the answer. To me calculating the odds using this type of probability is nothing more than a mental game.
Here are some interesting facts. With respect to the children did you know that there is a bias towards having more males born than female? And with respect to the coin flipping did you know that there is a bias towards the coin landing on the same face that it started? If you read the article there is 5% more males than females and 1% bias towards a coin flip.
I even argue if you could perform the coin flipping experiment in a vaccum under controlled circumstances then the 50/50 probability theory would fall flat on its face. What you should notice is that often when problems involving coin tosses are created they say the coin toss is fair. In other words you are jigging the conditions to get the response you want. Very few times in reality have I been able to say “fair conditions.”
I am a bigger fan of the scientific method and statistical probability. The math differences between theoretical probability and statistical probability is quite a bit. With statistical probability your main concern is about figuring out whether or not your experiments are consistent and whether or not they have a bias in them.
I especially like the following comment from the scientific method HTML page:
Statistics: How much of a difference is really a difference? If you flipped a coin 100 times, it should turn up heads half the time and tails the other half. However, it seldom actually turns out this way. If a person claimed to have psychokinesis (the ability of the mind to directly effect matter) and attempts to use the power of their mind to control the toss of a coin to make it turn up heads, would you conclude that they really could control the coin toss if they tossed it 100 times and it came up heads 51 times and tails only 49? What if it turned up heads 60 times and tails 40 times? What if it turned up heads 90 times and tails only 10? All of these outcomes could occur by chance. To determine what that chance is, scientist use statistics.
If something can occur one time in 55 million, it probably will. This is the probability that a person will win the Power Ball. Over time, one ticket in 55 million will win the Power Ball. If a scientist is conducting an experiment and the results can turn out a certain way one time in 55 million, it just might occur. Repeating the experiment will show if the results you obtained were just lucky results. Statistics will also show this.
For the past several months I have been writing my own trading software and I very quickly realized what works and did not work. I found it out by trial and error, but much of what I learned by stumbling around is written in the book Evidence-Based Technical Analysis.
The book helped me express my thoughts in my software in a structured manner. I knew that probability and the classical mathematics were not working. And I knew that I had to use statistics, but I kept bumping into a wall when I tried to put everything together. Reading this book with the following other books will help you get an overview of the maths; Options, Futures, and Other Derivatives, and Inside Volatility Arbitrage.
I recommend Evidence-Based Technical Analysis for anybody who is writing software that helps you trade.